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Sunday, 2 June 2013

Propositional Form

I suggested in Wittgenstein's
Toolkit that one way to view the Philosophical
Investigations is to see sections 1-133 as demolishing the “traditional”
approach to philosophy (exemplified by the Tractatus)
in order to establish a radically new method, which the rest of the book then puts
into practice. But this is just a rough guide, and of course things are not
quite as clear-cut as the distinction suggests.

For a start, §134
does not confront some big, sexy philosophical issue like free will or the
nature of consciousness. Instead it begins a brief, curious discussion of the
sentence “This is how things are”. Readers unfamiliar with the Tractatus are likely to be completely
baffled. Of all the possible topics, why pick on this banal, inoffensive little
statement? Actually, however, although the transition is rather abrupt there
has already been a certain amount of (easy to miss) stage-setting. First, the
topic is glanced upon in §65 when Wittgenstein’s interlocutor accuses him of taking
the easy way out:

“You talk about all sorts of language-games, but have
nowhere said what is essential to language-games, and so to language [….] So
you let yourself off the very part of the investigation that once gave you the
most headache, the part about the general
form of the proposition and of language.”

Mention of propositional from leads
to Wittgenstein’s account of family
resemblance concepts (and that account will be highly relevant here).

Then, at §114
Wittgenstein quotes directly from 4.5 of the TLP: “The general form of propositions
is: This is how things are.” His subsequent comment is typically cryptic: “That
is the kind of proposition one repeats to oneself countless times. One thinks
that one is tracing nature over and over again, and one is merely tracing round
the frame through which we look at it.”

That remark is also relevant to
the discussion in §134, but for present purposes the thing to remember is
that the idea of propositional form was of central importance to the Tractatus. There Wittgenstein had attempted
to sum it up in the phrase “This is how things are” (in German, “Es verhält
sich so und so” – see the postscript below for a discussion of the translation).

Why was this idea so important?
Well, it was an attempt to capture the very essence
of language itself – to reveal at a stroke its necessary structure, the one
thing common to all forms of linguistic communication, and which distinguishes
them from mere arbitrary sounds or scratches on a page. Moreover, according to
the Tractatus propositions work by
mirroring (on the one hand) the thoughts they express and (on the other hand)
the states of affairs they represent. So by revealing the essential structure
of the proposition you at the same time
reveal the essential structure of both thought and the world. In his notebook
of 1915 Wittgenstein wrote that it would provide “the nature of all facts […]
the nature of all being”.

That’s an astoundingly
ambitious claim, and it’s perhaps hard to see how so much metaphysical weight
could be supported by a phrase as unremarkable as “This is how things are”. But
for Wittgenstein (in the Tractatus)
it captured the proposition’s essential features in a pure and condensed form:
it showed that a proposition was a picture of a possible state of affairs (ie,
it asserted that something was the case); that it was a complex in which simple
names were linked in accordance with logical syntax (and this logical syntax in
turn mirrored the logical structure of the world); and that it was an essential
feature of a proposition that it could be assigned a truth-value – it was true if it pictured a possible state of
affairs which obtained and false if it pictured a possible state of affairs
which didn’t obtain.

So although at first blush
“This is how things are” seems a trivial, empty formulation, the more you
unpack its implications the more it seems to take on an emblematic, almost mystical, status. As §114
mentions, you can find yourself repeating it over and over while straining to
see with absolute clarity the relationship between language and the world:
“This is how things stand, this is how things stand, this is how things stand….”

And it is to this totemic
sentence that Wittgenstein turns in §134. So just when we seemed set to
move into new territory we get one of the most backward-focused discussions in
the whole of the Investigations. On
the plus side, however, at least it seems we’re in for something momentous; having
already attacked the TLP’s general approach, Wittgenstein is now going to
strike at its very heart. Isn’t he? On the contrary! Rather than some “clash of
the Titans”, §134
provides one of the most striking examples of bathos to be found in philosophy.

He starts by asking why he was
tempted to see “This is how things are” as the general form of the proposition.
Two reasons are offered: 1) it is itself a sentence and therefore an example of
the phenomenon he was seeking to explain; and 2) it is commonly used as a kind
of “schema” – a variable which stands in for a set of specific sentences. These
two aspects would seem to leave it well placed to carry out its required role.
But against this he makes two observations. First, there is nothing
compellingly precise about the form of words chosen in the Tractatus. Any number of alternatives might’ve done just as well
(eg, “such and such is the case” or “things are thus and so”) – indeed, even a
single letter (“p”) could be used, as happens in formal logic. Of course, it
would be ridiculous to call “p” the general form of the proposition, but this
just goes to show how the schematic aspect of “This is how things are” fails to
justify the metaphysical status allotted to it in the Tractatus. Indeed, its very role as a variable makes it atypical.

This atypical quality is
brought home by Wittgenstein’s second observation: there is no such thing as
comparing “This is how things are” with reality in order to see if it is accurate.
And yet functioning as an object of comparison is supposedly an essential
aspect of propositions (TLP 4.05)! Without the possibility of comparison a
proposition cannot be assigned a truth-value (TLP 4.06). So the phrase chosen
to represent general propositional form fails to exhibit one of its (alleged) primary
characteristics. And if that’s so, how can “This is how things are” be called a
proposition at all? Now, the
Wittgenstein of the Tractatus
might’ve agreed with this point and replied that “This is how things are” was a
meaningless form of words which attempted to say what could only be shown
(and here an obscure metaphysical theory is being defended by an even more
baffling one). In the Investigations,
however, Wittgenstein sees no need for such obscurities; unlike “p”, “This is
how things are” is a well-known phrase with an uncontroversial use in our language. He concludes with
withering irony: “so it illustrates the fact that one feature of our concept of
a proposition is sounding like one”.

So the sound (or look) of a
proposition is part of our concept of what a proposition is. That’s why we’re
not troubled by calling (eg) “I sing the body electric” a proposition even
though its meaning is obscure at best. (But what about “Joob wa stu”? Or “Gdk
rrrx pypy”?) And the “conventional” or “familiar” form of “This is how things
are” was one of the (unacknowledged) factors behind claiming it as the general
form of the proposition. But of course this familiarity is a contingent feature
of our particular language. In terms of the role the sentence plays it’s
possible to imagine it being replaced by “p”, or an underscore, or even a hand
gesture. But would we even have been tempted
to take Wittgenstein seriously if TLP 4.5 had stated “The general form of the
proposition is: ___”? Thus the grand metaphysical pronouncement which was to
lay bare “the nature of all being” turns out to be (at least in part) almost
comically human.

But if we’re going to reject
the idea of propositional form, how can we account for the fact that we can and
do recognise propositions and distinguish them from other sounds or marks on
the page? This, of course, brings us back to the notion of family resemblance
concepts, as §135
makes clear. It links not just to §65 but also to §23, where Wittgenstein stresses
the endless variety of kinds of sentence. There is no one thing common to all
propositions. Instead, there are an overlapping series of similarities that for us mean it makes sense to group them
all under the same concept-word. If you have doubts about this, it’s relatively
simple (yet instructive) to produce a list of propositions which vary in terms
of their form and function. Here’s mine:

The pen is on the table.

All men are mortal.

I am in pain.

Every rod has a length.

King Lear
is more profound than Hamlet.

Heroin is better than sex.

Stately, plump Buck Mulligan came from the
stairhead, bearing a bowl of lather on which a mirror and a razor lay crossed.

A fool and his money are soon parted.

2x2=4.

E=MC²

a=a

Confronted with the facts, the
metaphysical theory looks to be in trouble. But §136 considers an alternative
attempt to validate it by focussing on the concept of truth-functionality. To
be honest, I find it a tricky, frustratingly cursory section, but my reading of
it is as follows.

First, we’re reminded that
truth-functionality as a necessary feature of propositions was one of the
things Wittgenstein tried to capture in “This is how things are”, and in doing
this he was (he felt) describing a necessary truth about language and its
connection to the world. So “Such and such is true (or false)” would’ve been
another way of expressing general form. But if
language is conceived of as a rigid calculus (as was the case in the Tractatus) then this new formulation
becomes problematic because “’p’ is true = p”. The “is true” part adds nothing;
it is a redundant clause. Of course, in language as it is actually used (ie,
not as a rigid calculus) “’p’ is true” is not
a pointless elaboration of p. “It’s true that I lied to you” doesn’t have the
same use as “I lied to you”. In fact,
it doesn’t even always have the same use as “I lied to you. It’s true.” So
either way “Such and such is true” fails to capture essence. From the point of
view of language as a calculus the “is true” part is redundant, and from the
point of view of use it is just another tool in the box rather than an
expression of necessary structure.

That’s not to say, however, that
we can’t decide to adopt a definition such as “A proposition is whatever can be
true or false”. We might do so when we wished to use “proposition” in a technical
sense as something distinct from other types of sentences. So (on this basis)
“Give me a dollar” is not a proposition but “I gave you a dollar” is. The technique of asking “can it be called
true (or false)?” might be useful here in telling one from the other, rather
like the trick used to see if a large number is divisible by 3 (see §137).
It should be noted, however, that since “proposition” is a family resemblance
concept the meaning of assigning a truth-value will vary from case to case.
Consider, for example, the varying significance of replying “that’s true” or “that’s
false” to the following:

Paris is the capital of France.

2+2=4.

Virtue is its own reward.

A thing is identical to itself.

One might say “the kind of
truth is the kind of language-game” (cf PI Part II, §332).

But the temptation here is to
assume that the phrase “A proposition is whatever can be true or false” discovers something about the world. Wittgenstein’s
discussion of this temptation focusses on the notion of truth and falsity fitting the concept of the proposition –
presumably because that was the form the temptation had taken in his particular
case. It is, so to speak, a suggestive
form of words, conjuring up the notion of “true” and “false” as jigsaw pieces
which only and always lock into another piece labelled “proposition”.

One can see how this way of
looking at things might lead to puzzlement. For example, it suggests that truth
and falsity exist independently of propositions, even though they can interact
with nothing else. What sort of thing, then, is truth? In what sense does it exist? Are we talking about a
Platonic Form here? Or something akin to a soul? Or should we say that truth
and falsity do not exist independently of propositions but that the expression
of a proposition necessarily calls them into being? But how might that happen? How
can it be that truth and falsity must
come into being with the proposition even though they are distinct from it? –
For it cannot be an accident that the
two are connected in the way they are, as if it might just as easily have been
otherwise. But what is the nature of this necessary connection? Are we talking
about a pre-established harmony here? And what does that even mean? And so on.
The whole thing is starting to look thoroughly mysterious.

At this point Wittgenstein
brings things down to earth by pointing out that the phrase “only a proposition can be true” is merely a
potentially misleading way of saying “we predicate ‘true’ and ‘false’ only of
what we call a proposition” (§136). In other words, it is the
expression of a rule – a grammatical
remark disguised as a description. (Re-read §114 now and you will see the
relevance of the comment there about TLP 4.5. In fact, §114 is an aphoristic version of
the point made in §50. See also "The
Death of Metaphysics" for more on this.) What we thought was a
startling, almost mystical, discovery
– a truth about the world that could not logically
be false – turns out to be nothing more than a definition enshrined in a
typically idiomatic form of expression.

And now we can see where the
puzzling sense of necessity came from: it was linked to the categorical nature
of rules. They say “You must do
things this way if you want to play the game. If you don’t then you’re playing
the game wrong – or else you’re playing a different game altogether”. The
hardness of the metaphysical “must” is a misunderstanding, a shadow cast by
grammar.

Ultimately, then, Wittgenstein
attacks the notion of propositional form as a typical example of the “sublimation”
of our language (cf "Logic and
Magic"). The formula presented in the Tractatus failed to do its job not because it was poorly
constructed but because there was no such
job to do. The problem, therefore, lay not so much with theory expressed as
with the background assumptions which committed the young Wittgenstein to a
particular way of seeing things. The Tractatus
was merely an attempt to systematically work through the implications of those
assumptions. They themselves went unquestioned – indeed, it never even occurred
to him that they might be problematic (cf §308: “The decisive movement in
the conjuring trick has been made, and it was the very one that seemed to us
quite innocent”). This attempt to dig beneath the surface of an argument and locate
the crucial difficulty at deeper level is entirely characteristic of the Philosophical Investigations. I mentioned
at the start that Wittgenstein doesn’t tackle a big “sexy” issue in §134.
In fact, he never directly does. For him, the problem lies not so much with
what (eg) Empiricists and Rationalists argue about as with the assumptions that
neither side question. Those assumptions are his real target. But so far he has
barely scratched the surface.

Postscript: translating “Es
verhält sich so und so”

I think there are problems with
the translation of “Es verhält sich so und so”. For one thing, it’s irritating
that the Investigations and the two
major English translations of the Tractatus
each offer a different version. Ogden’s 1922 translation of the Tractatus gives us “Such and such is the
case”; then Anscombe’s 1953 translation of the Investigations gives us “This is how things are” (retained in all
subsequent editions); and then the 1961 Pears/McGuiness Tractatus gives us “This is how things stand”. (Duncan Richter’s 2009
student edition provides a fourth variation: “Things are thus and so”.)

I’m not saying that any one of
those is wrong, but at the very least the diversity creates issues for English-language
readers which don’t exist in the original German. For one thing it means that
if you come to the Investigations
already familiar with the Tractatus you’ll
be wrong-footed by the new rendering. I imagine that it’s easy for someone used
to Ogden’s Tractatus to completely
miss the reference in §134. On the other hand, those who’ve read Pears/McGuiness will
get the reference but be irritated by the (frankly) pointless switch from
“stand” to “are”. (Though of course Anscombe’s “are” came before
Pears/McGuiness’ “stand” – was the change due to a copyright issue? It would be
a shame to think so.) Either way, it dilutes the Investigations on an aesthetic level. For when Wittgenstein opened §134
with “Betrachten wir den Satz: “Es verhält sich so und so” he surely assumed
that his readers would be familiar with the Tractatus
and that their ears would prick up at the mention of this famous phrase. But if
there’s no agreement as to what that “famous phrase” actually was then everyone’s ears are going to remain
firmly in the “down” position.

It’s also important to realise
that the different translations have philosophical implications. For example,
it puzzled me for a long time that (in Anscombe’s translation) §134 claims
“This is how things are” is used as a schema.
You can just about see what this is getting at, but really that’s not the most obvious use suggested by
the phrase. It more commonly functions as a prefix to a statement, and implies
that the speaker is cutting to the heart of the issue. So someone might say “This
is how things are: unless we can raise £5,000 by midnight we’ll lose the house”.
For the phrase to work as a schema you have to imagine a strong emphasis on “this”,
together (perhaps) with a hand-gesture suggesting the various things to which “this”
refers. So it would be “This […] is
how things are” with the gesture providing the “[…]”. That’s a bit of a stretch
and, in any case, it seems to me that it’s now the gesture which is doing the
schematic work rather than the actual words.

Of course, if you substitute (eg)
“Things are thus and so” then the schematic aspect becomes much more obvious. (Mind
you, I can’t help reflecting that English already has a well-established verbal
schematic, namely: “blah, blah, blah”. I suppose it might’ve caused uproar if
TLP 4.5 had stated “The general form of the proposition is: Blah, blah, blah”.)
The problem with the “thus and so” version (so far as I can see) is that it
doesn’t capture the declarative nature of propositions as strongly as “This is
how things are”. This is an important element because it stresses the
truth-functional nature of propositions. If I utter the words “the cat sat on
the mat” merely because I like their sound then there’s no question of me being
right or wrong. But if I assert that
the cat sat on the mat then that’s either true or false. For this reason, I
find it more useful to bear in mind Anscombe’s version when considering §136,
which discusses the link between propositions and truth-functionality.

Having said that, it’s not as
if the assertive element is absent
from “Things are thus and so”; it’s merely less emphatic (because the “are”
comes in the middle of the sentence rather than at the end). All in all I find “Things
are thus and so” to be closer to the original (I also prefer it to Ogden’s “Such
and such is the case”). I wonder why Anscombe changed Ogden’s version, why
Pears/McGuiness pointlessly varied Anscombe’s version and why the Hacker/Schulte
4th Edition of the Investigations
stuck to Anscombe’s version even though Hacker clearly has issues with the
wording and suggests “Things are thus and so” as a more helpful alternative (see
Wittgenstein: Understanding and Meaning,
chapter XVI). I’d be interested to hear any views on the subject.

10 comments:

great post. Brought back to me memories of my youth and a Baker and Hacker seminar where Baker I think it was suggested that the general form of the proposition was in fact: "That's the way the cookie crumbles". Your "Blah, Blah, Blah" is a nice addition :-)

Actually (now I think about it) "blah, blah, blah" is interesting because it works as a schema despite the fact that it's not a sentence - indeed it doesn't even contain any "real" words. It "sounds" like a proposition, but not in the way "This is how things are" does. That is, it mimics (or suggests) the sound of someone waffling on. You might say it was at the very "outer edge" of sounding like a proposition. And yet it works just fine for all that.

well i love plans! not unlike many, i suppose, i've been overly focused on 1-133 over the years i've read and reread the damn thing. i think that that's the only stretch in which conventional, structuring features can be found (they're where you would think they are - the beginnings of 65, 89, less prominently so at a few other places). but that view has left me with some work to do to explain how 134 onward work if not organized by the same sorts of structuring features.

Certainly the structure is looser after 133, but I think there is a flow to the argument. On the other hand, the book certainly kind of drains away into the sand, but that's as much to do with Wittgenstein's therapeutic conception of philosophy as anything. It doesn't tend to result in neat conclusions.

i certainly don't disagree with that, i had in mind literary or rhetorical features more than dialectical ones. if anything the trouble is that there's so much flowing! (eddying, even.)

i have gone ahead and reread despite myself, and i'm struck by how definite the appearance has been, after 134, of concern with both the a priori (or relatives, like grammar) and with exprience or the empirical. i haven't gone back to scrutinize §§1-133 (to see if concern with those topics is relatively absent), but that shift after §134, at least, sure seems to lend interpretative support to your tying a major point of departure from there to the tractatus.

I don't want to get ahead of myself, because this is one of the things I hope to mention in my next post, but it seems to me that from 134 onwards (and particularly from 138 onwards) Wittgenstein tackles the deep-rooted temptations that lay beneath the theories of the TLP. They're not mentioned in the Tractatus itself precisely because they were taken for granted.

Sorry, that didn't directly address your point. It seems to me that 1-133 are very much concerned with criticising philosophy as a study of the a priori and moving instead towards a study of how words are used. It flows directly from the idea that meaning is use and is summed up in the striking phrase "Don't think, look!"